Summary

This report addresses the assessment of the extent to which the racial composition of North Carolina boards of county commissioners represent that of their respective counties. I have used a simulation of random selections from the 2016 NCSBE voter turnout in this assessment. This study uses four race categories, American Indian, Black, White, and Other. The simulation results in identifying over one-half the counties where the actual 2016 board of county commissioners racial composition, as reported by the NCACC, was representative of the county population. To a significant extent this follows from there being thirty four counties that have fewer than ten percent Black residents, where accordingly there are few likely outcomes. I also utilize a diversity index to make semi-quantitative statements about the counties. The simulation and the diversity methods are independent of each other, providing two ways to assess representation. This analysis suggests that there are nineteen counties where the computed lack of representation merits further study.

Methodology

The purpose of this report is to assess the representativeness of the racial composition of boards of county commissioners with respect to that of their constituents. I will first utilize a methodology that treats this as a combinatorial problem, where the results of sampling constituents is compared to board compositions. The sampling is carried out by use of simulations based on either Census Bureau American Community Survey estimates, or NCSBE voter turnout records, and is compared with NCACC board compositions.

An inherent property of simulations is the variability of results. This variability is a consequence of the use of different randomization seeds, and also from using different numbers of simulation runs. This is compounded by the population estimates, which are indeed, just estimates. Even in the decadal censuses, populations are estimates. Another contributing factor is that race reporting is shaped by being self-reported and using categories that are somewhat different for the Census Bureau, NCSBE,and possibly for the NCACC.

As a consequence of this, results from simulations must not be over-interpreted. Small differences in the assessments between counties or over years, are of minor consequence. “Small”, however, needs to be determined as the analysis progresses. Practically, this mitigates against rank ordering of counties on the basis of simulation results. It argues towards using quartiles, which while requiring ranking presents gross rather than fine results, as well as for repeating simulations using different seeds and number of runs.

Population and Voter Turnout Aspects of North Carolina

In order to constructively respond to the question of the representativeness of boards of county commissioners, I will provide some information about the demographics of North Carolina population and voter turnout. For the purposes of this report, I will use data for 2016 unless otherwise stated.

The plot below shows the 2016 Black population percentage against the total population, by county. There were 34 counties with under 10% Black population. Those counties constitute 20% of the total population of the state. On the other hand, there were 0 counties with under 10% White population. Counties with a small population of any race are mathematically challenged to have a matching board composition.

The next plot looks at 2016 voter turnout. It shows the percentage of all the voters by county who self-reported as Black when their voter registration was recorded. There were 37 counties with under 10% Black of the total voter turnout. Those counties constitute 23% of the total voter turnout of the state. On the other hand, there were 0 counties with under 10% White of the total voter turnout. Counties with a small turnout of any race are mathematically challenged to have a matching board composition.

As a final step in this section, I show below the association between the Black population percentage and the Black voter turnout percentage, a combining of the two previous plots. There are a small number of counties that show appreciable deviations from equality, that is, the distance from a straight line of slope 1, passing through the origin. This infers that using either population or voter turnout in simulations should give similar results. It remains necessary to verify this.

Population and Voter Turnout Simulations

The basis for this current investigation of county commissioner representation is based on simulations. Each county board is described by the counts of American Indian, Black, and White commissioners provided by the NCACC. These three categories are the only ones provided in the NCACC data. I will assign a count of zero to the category Other when using in the NCACC data.

The board compositions are compared with combinatorial probabilities computed by simulation, using NCSBE records of voter turnout. There are misalignments, or at least ambiguities, between the race categories provided in various data sources. I attempt to deal with that by reducing race categories to American Indian, Black, White, and a catchall of Other. As I have time for it, I will try to estimate the errors due to the different ways of tallying race. However, we are dealing with estimated population figures, and self-reported, category-limited, NCSBE and NCACC data. The best we can do is make estimates that are clearly documented. Of more substance, I will undertake to separate and compare the population and turnout simulations with the intention of detecting what significant differences there might be.

Any comparison of board composition to turnout is confronted with the small number of board members in each county. In 2016, there were 62 counties with five commissioners, 31 with seven, and 5 with more than seven. A county with five board members of two races necessarily has only 0:5, 1:4, or 2:3 composition. This means that if the county turnout is 50:50, the board proportions cannot match the county very well. The simulations will, of course, reflect this, and it will be necessary to utilize techniques other than simple comparisons to characterize representations.

This report uses a simulation of 5000 runs per county, based on the NCSBE voter turnout data. To start this, I will look at the behavior of the board simulations for some selected counties.

Consider first Anson and Washington. These are small counties with similar proportions of Black residents. Npct is the percentage of times that a particular board composition was generated. The results show what is mathematically necessary, namely that for Anson 4 Black, 3 White is as likely as 3 Black, 4 White, and similarly for Washington 3 and 2 is as likely as 2 and 3.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Anson 10598 0.1 42.1 46.0 11.8 7 0 4 3
Washington 6178 0.1 48.6 48.7 2.6 5 0 3 2


  1. Anson 7 Members
  1. Washington 5 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 3 1 12.08 0 3 2 0 27.30
0 3 4 0 10.88 0 2 3 0 25.80
0 4 3 0 10.56 0 4 1 0 14.66
0 2 4 1 10.50 0 1 4 0 13.40
0 4 2 1 8.06 0 2 2 1 4.68
0 2 5 0 7.42 0 0 5 0 3.14
0 5 2 0 6.00 0 5 0 0 3.10
0 2 3 2 5.14 0 3 1 1 2.82
0 3 2 2 4.74 0 1 3 1 2.60
0 1 5 1 4.36 0 0 4 1 0.70
0 5 1 1 2.90 0 4 0 1 0.62
0 1 6 0 2.66 0 2 1 2 0.28
0 1 4 2 2.34 0 1 2 2 0.20
0 4 1 2 2.24 0 0 3 2 0.12
0 6 1 0 1.98 1 1 3 0 0.12
0 2 2 3 1.18 1 2 2 0 0.12
0 1 3 3 0.90 1 3 1 0 0.12
0 0 6 1 0.78 0 3 0 2 0.06
0 3 1 3 0.78 1 0 4 0 0.06
0 0 5 2 0.70 0 2 0 3 0.04
0 0 7 0 0.64 1 1 2 1 0.02
0 6 0 1 0.54 1 2 1 1 0.02
0 5 0 2 0.38 1 4 0 0 0.02
0 4 0 3 0.32 NA NA NA NA NA
0 2 1 4 0.24 NA NA NA NA NA
0 1 2 4 0.22 NA NA NA NA NA
0 0 4 3 0.18 NA NA NA NA NA
0 7 0 0 0.16 NA NA NA NA NA
1 3 3 0 0.16 NA NA NA NA NA
1 2 4 0 0.14 NA NA NA NA NA
1 2 3 1 0.12 NA NA NA NA NA
1 1 3 2 0.08 NA NA NA NA NA
1 1 4 1 0.08 NA NA NA NA NA
1 4 2 0 0.08 NA NA NA NA NA
0 0 3 4 0.06 NA NA NA NA NA
0 3 0 4 0.06 NA NA NA NA NA
1 1 5 0 0.06 NA NA NA NA NA
1 2 2 2 0.06 NA NA NA NA NA
1 3 2 1 0.06 NA NA NA NA NA
1 3 1 2 0.04 NA NA NA NA NA
1 6 0 0 0.04 NA NA NA NA NA
1 0 4 2 0.02 NA NA NA NA NA
1 3 0 3 0.02 NA NA NA NA NA
1 4 0 2 0.02 NA NA NA NA NA
1 4 1 1 0.02 NA NA NA NA NA



Cumberland and Durham are both large. The following table shows the turnout-based simulation for these counties.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Cumberland 128007 0.9 42.2 46.5 10.4 7 0 3 4
Durham 156843 0.2 36.2 52.1 11.4 5 0 2 3


  1. Cumberland 7 Members
  1. Durham 5 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 4 0 12.26 0 2 3 0 18.54
0 4 3 0 11.12 0 1 4 0 13.48
0 3 3 1 10.42 0 3 2 0 13.20
0 2 4 1 10.10 0 2 2 1 12.04
0 2 5 0 8.24 0 1 3 1 11.40
0 4 2 1 7.18 0 3 1 1 5.46
0 5 2 0 6.18 0 4 1 0 5.00
0 2 3 2 4.06 0 0 5 0 3.94
0 1 5 1 4.04 0 1 2 2 3.72
0 3 2 2 3.48 0 0 4 1 3.66
0 1 6 0 3.32 0 2 1 2 2.84
0 1 4 2 2.48 0 0 3 2 1.70
0 5 1 1 2.18 0 4 0 1 0.98
0 4 1 2 1.72 0 3 0 2 0.76
0 6 1 0 1.66 0 1 1 3 0.68
1 2 4 0 1.00 0 5 0 0 0.50
0 2 2 3 0.96 0 0 2 3 0.44
1 3 3 0 0.90 0 2 0 3 0.26
1 3 2 1 0.86 1 1 3 0 0.26
0 1 3 3 0.80 1 0 3 1 0.24
1 2 3 1 0.76 1 2 2 0 0.20
0 0 6 1 0.62 1 3 1 0 0.16
1 4 2 0 0.52 1 0 4 0 0.14
0 0 5 2 0.50 1 1 2 1 0.10
0 3 1 3 0.50 0 0 1 4 0.08
1 1 4 1 0.48 1 2 1 1 0.06
0 5 0 2 0.42 0 1 0 4 0.04
0 6 0 1 0.38 1 1 1 2 0.04
0 7 0 0 0.34 1 3 0 1 0.04
0 0 7 0 0.32 1 0 1 3 0.02
1 2 2 2 0.30 1 4 0 0 0.02
1 1 5 0 0.28 NA NA NA NA NA
1 4 1 1 0.26 NA NA NA NA NA
1 0 5 1 0.14 NA NA NA NA NA
1 5 1 0 0.14 NA NA NA NA NA
1 1 3 2 0.12 NA NA NA NA NA
0 0 4 3 0.10 NA NA NA NA NA
0 1 2 4 0.10 NA NA NA NA NA
1 0 4 2 0.10 NA NA NA NA NA
0 4 0 3 0.08 NA NA NA NA NA
1 0 6 0 0.08 NA NA NA NA NA
0 2 1 4 0.06 NA NA NA NA NA
1 1 2 3 0.06 NA NA NA NA NA
1 3 1 2 0.06 NA NA NA NA NA
0 3 0 4 0.04 NA NA NA NA NA
1 3 0 3 0.04 NA NA NA NA NA
1 4 0 2 0.04 NA NA NA NA NA
1 6 0 0 0.04 NA NA NA NA NA
2 3 2 0 0.04 NA NA NA NA NA
0 0 3 4 0.02 NA NA NA NA NA
1 0 3 3 0.02 NA NA NA NA NA
1 2 1 3 0.02 NA NA NA NA NA
1 5 0 1 0.02 NA NA NA NA NA
2 1 4 0 0.02 NA NA NA NA NA
2 2 2 1 0.02 NA NA NA NA NA



Another duo of counties, distinguished by being the largest in the state, are Mecklenburg and Wake.

County Total AmIndPct BlackPct WhitePct OtherPct ncomm namin nafam nwhite
Mecklenburg 475593 0.2 31.1 59.3 9.4 9 0 4 5
Wake 531248 0.2 18.1 69.3 12.3 7 0 2 5


  1. Mecklenburg 9 Members
  1. Wake 7 Members
AmInd.1 Black.1 White.1 Other.1 Npct.1 AmInd.2 Black.2 White.2 Other.2 Npct.2
0 3 6 0 10.84 0 1 5 1 14.48
0 2 6 1 10.00 0 1 6 0 14.48
0 3 5 1 9.94 0 2 5 0 11.70
0 4 5 0 8.88 0 2 4 1 9.70
0 2 7 0 8.64 0 0 6 1 9.32
0 4 4 1 6.50 0 0 7 0 7.28
0 1 8 0 5.30 0 1 4 2 6.58
0 2 5 2 5.02 0 0 5 2 5.18
0 5 4 0 4.88 0 3 4 0 4.58
0 1 7 1 4.78 0 2 3 2 3.48
0 3 4 2 4.02 0 3 3 1 3.42
0 1 6 2 2.78 0 1 3 3 1.86
0 5 3 1 2.66 0 0 4 3 1.52
0 4 3 2 2.28 0 4 3 0 1.04
0 0 8 1 1.58 0 3 2 2 0.80
0 6 3 0 1.52 0 4 2 1 0.68
0 1 5 3 1.06 0 2 2 3 0.46
0 2 4 3 1.06 1 2 4 0 0.38
0 0 7 2 1.04 0 5 2 0 0.34
0 0 9 0 0.96 1 1 5 0 0.34
0 3 3 3 0.84 0 0 3 4 0.28
0 6 2 1 0.78 1 0 5 1 0.26
0 5 2 2 0.64 1 0 6 0 0.26
0 4 2 3 0.36 0 1 2 4 0.24
1 3 4 1 0.32 1 1 4 1 0.20
0 0 6 3 0.28 0 3 1 3 0.16
0 2 3 4 0.28 1 0 4 2 0.14
1 2 5 1 0.28 0 4 1 2 0.12
1 3 5 0 0.26 1 2 3 1 0.12
0 1 4 4 0.24 0 5 1 1 0.10
0 7 2 0 0.22 1 1 3 2 0.08
1 4 4 0 0.22 1 3 3 0 0.08
1 4 3 1 0.16 0 6 1 0 0.06
0 5 1 3 0.14 1 2 2 2 0.06
1 1 6 1 0.14 1 3 2 1 0.06
1 1 7 0 0.12 0 2 1 4 0.04
1 2 4 2 0.12 0 0 2 5 0.02
0 7 1 1 0.10 0 1 1 5 0.02
1 2 6 0 0.10 0 3 0 4 0.02
0 3 2 4 0.08 1 0 3 3 0.02
0 6 1 2 0.08 1 2 1 3 0.02
1 1 5 2 0.08 2 0 4 1 0.02
1 3 3 2 0.08 NA NA NA NA NA
0 8 0 1 0.04 NA NA NA NA NA
1 0 6 2 0.04 NA NA NA NA NA
1 0 7 1 0.04 NA NA NA NA NA
1 0 8 0 0.04 NA NA NA NA NA
1 2 3 3 0.04 NA NA NA NA NA
1 5 2 1 0.04 NA NA NA NA NA
1 5 3 0 0.04 NA NA NA NA NA
0 0 5 4 0.02 NA NA NA NA NA
0 1 3 5 0.02 NA NA NA NA NA
0 4 1 4 0.02 NA NA NA NA NA


Clusters

Which counties had boards that did, or did not, well-represent the racial composition of the turnout? What objective criteria can we establish? I will use clustering, which is a mathematical approach to sweeping together simulated board compositions that have nearly the same probabilities. It is far from simple to compute clusters. Briefly, for this analysis, I will use the R package Ckmeans.1d.dp. Picture, then, a histogram of the percentage of the simulation runs that resulted in each board compositions, Npct. Now arrange this histogram in descending order by Npct. The computation starts with supposing that there are a small number k of clusters, perhaps three to five. It proceeds to find k (or fewer) positions for the Npct such that the within cluster sum of squares to each cluster mean (withinss) is minimized. This takes a lot of work and I depend entirely on the sagacity of the authors of that package. I will number the clusters from left to right, that is, cluster 1 will correspond to the grouping of the highest values for Npct. Not all data is amenable to cluster analysis - the flatter the distribution of the variable of interest, the less well can it be said to have clusters. The Appendix pursues withinss at more length.

I will use the clusters computed for the board composition simulations based on turnout estimates of all the counties. Using both three and five cluster targets, I will determine the cluster number for the actual 2016 board compositions. I have already mentioned that there were 34 counties with under 10% Black population. It seems reasonable to expect that there would be good matches for these counties since there are few choices other than all White commissioners. In light of this I will note counties as being over or under 10% Black population proportion when that seems useful.

For five clusters the fit to the first cluster, where the actual board composition matches well with the turnout, we have:

over10 Cluster N
NO 1 35
NO 2 1
NO 3 1
YES 1 33
YES 2 24
YES 3 1
YES 4 3
YES 5 2



Three clusters shows much the same. Having this smaller number of clusters might be a better aid to assessing comparability. I will continue this report using the three cluster data.

over10 Cluster N
NO 1 35
NO 2 2
YES 1 46
YES 2 12
YES 3 5



It is evident that there are 81 counties for the three cluster computation and 68 for the five cluster configuration whose 2016 board compositions match the turnout simulation cluster 1. That is, the simulation appears to announce that at least 68% of the counties had representative board compositions.

Which counties with over 10% Black population are in the clusters? I will provide this information as two separate lists, one for those in cluster 1, another for those in clusters 2 and 3. The following table shows the counties with over 10% Black population that are in the most representative cluster. There are some oddities in this list. For instance, Robeson County is included even though Npct (the percentage of times that the simulation resulted in the actual board composition) is only 6.74%. An interpretation in the case of Robeson is that, compared to many other counties, there are a large number of likely board compositions. Similar remarks can be made about other counties with low Npct.

These are the 46 counties in 2016 with over 10% Black population that are in cluster 1, the most representative of the three clusters:

County n_clus ncomm AmInd Black White Other Npct
Anson 1 7 0 4 3 0 10.56
Beaufort 1 7 0 2 5 0 23.64
Bladen 1 9 0 3 6 0 19.46
Cabarrus 1 5 0 0 5 0 25.48
Camden 1 5 0 0 5 0 38.80
Caswell 1 7 0 2 5 0 23.76
Chowan 1 7 0 2 5 0 26.18
Craven 1 7 0 2 5 0 20.94
Cumberland 1 7 0 3 4 0 12.26
Duplin 1 5 0 2 3 0 23.98
Durham 1 5 0 2 3 0 18.54
Edgecombe 1 7 0 4 3 0 25.80
Forsyth 1 7 0 2 5 0 20.06
Franklin 1 7 0 2 5 0 22.34
Gaston 1 7 0 0 7 0 20.58
Gates 1 5 0 1 4 0 24.96
Granville 1 7 0 2 5 0 21.62
Greene 1 5 0 2 3 0 28.38
Guilford 1 9 0 3 6 0 14.04
Halifax 1 6 0 3 3 0 20.62
Harnett 1 5 0 1 4 0 27.10
Hertford 1 5 0 4 1 0 26.28
Lee 1 7 0 1 6 0 20.82
Lenoir 1 7 0 2 5 0 20.18
Martin 1 5 0 2 3 0 32.78
Mecklenburg 1 9 0 4 5 0 8.88
Moore 1 5 0 0 5 0 45.72
Nash 1 7 0 2 5 0 19.76
Onslow 1 5 0 0 5 0 23.58
Orange 1 7 0 1 6 0 13.32
Pamlico 1 7 0 1 6 0 30.06
Pasquotank 1 7 0 2 5 0 21.48
Pender 1 5 0 0 5 0 33.30
Person 1 5 0 1 4 0 31.46
Pitt 1 9 0 3 6 0 17.12
Robeson 1 8 3 2 3 0 6.74
Rowan 1 5 0 0 5 0 36.14
Sampson 1 5 0 2 3 0 22.20
Scotland 1 7 0 3 4 0 15.32
Tyrrell 1 5 0 1 4 0 28.88
Union 1 5 0 0 5 0 35.88
Vance 1 7 0 4 3 0 22.06
Wake 1 7 0 2 5 0 11.70
Washington 1 5 0 3 2 0 27.30
Wayne 1 7 0 2 5 0 19.64
Wilson 1 7 0 3 4 0 19.04



Here are the 17 counties with over 10% Black population that are in clusters 2 and 3, the least representative of the three clusters:

County n_clus ncomm AmInd Black White Other Npct
Alamance 2 5 0 0 5 0 21.84
Bertie 2 5 0 2 3 0 19.68
Chatham 2 5 0 1 4 0 23.96
Cleveland 3 5 1 0 4 0 0.14
Columbus 2 7 0 1 6 0 18.90
Hoke 3 5 1 3 1 0 3.80
Hyde 2 5 0 0 5 0 28.42
Iredell 2 5 0 1 4 0 27.34
Johnston 2 7 0 0 7 0 19.58
Jones 2 5 0 0 5 0 11.26
Montgomery 2 5 0 0 5 0 24.18
New Hanover 2 5 0 1 4 0 25.72
Northampton 3 5 0 5 0 0 5.86
Perquimans 2 6 0 2 4 0 23.92
Richmond 3 7 0 0 7 0 4.06
Rockingham 2 5 0 0 5 0 26.28
Warren 3 5 0 5 0 0 4.12



Here are the counts of counties by number of simulated board compositions in cluster 1, first for the three cluster categorization:

Configs. in Cluster 1 N
1 59
2 31
3 5
4 4
5 1



Here for the five cluster categorization:

Configs. in Cluster 1 N
1 88
2 10
3 1
4 1


A Diversity Measure for Counties: Theil’s Entropy Index

Analysis of representativeness may benefit from use of an alternative to the combinatorial approach, that of a quantitative measure of diversity, one used by economists and social scientists. The measure I will use is called Theil’s Entropy Index, which comes from information theory. The Index measures diversity but in a way that does not distinguish between specific population groups. For example, in our case populations are composed of the four race categories American Indian, Black, White, and Other. The index would have the same value for 20% Black and 80% White, compared to 80% Black and 20% White - it measures diversity not matter how it is achieved. Theil’s Entropy Index, called H in this report, is computed as described in the next paragraph. I will do this for the board, and also for the county turnouts. These two indexes can then be compared.

Mathematically, the calculation looks like this: let pi be the proportion of race i, then H is the sum of \(p_i\cdot ln(1/p_i)\). If there are four categories and only one is present, then \(H=1\cdot ln(1)=0\). This is the least diverse, and has the lowest H. If the proportions are (0,0,0.2,0.8), then \(H=0.2\cdot ln(1/0.2)+0.8\cdot ln(1/0.8)\sim 0.50\). An even split between only two races (0,0,0.5,0.5) would result in \(H=2\cdot (0.5)\cdot ln(1/0.5)\sim 0.69\). If all are present equally, then \(H=4\cdot (1/4)\cdot ln(1/0.25)\sim 1.39\). If there are N categories, H varies between 0 for the least diversity to ln(N) for the most uniform, which can be called the most diverse. In our case, N=4, so the maximum H is 1.39.

Counties collect in more-or-less horizontal lines because boards are small in size and, accordingly, there are only a few realizable values for their diversity index. Counties with boards that have a zero diversity index have members of one race only. Speaking in general terms, it would be desirable to have board diversity comparable to that of the county turnout. This would put the data points in the next plots near the diagonal line, where the county and the actual board diversities would be the same.

The next plot utilizes data for all one hundred counties. Even though the diversity measure is entirely independent of the clustering we used previously, it may be of interest to identify the counties by which cluster they were in. That is what is embodied in this plot.

The 52 counties with Board Diversity Index of zero (that is, where the board is composed of members of a single race category) are shown below in order by Hcty, the turnout Diversity Index, with their turnouts and 2016 board compositions. Since these counties have boards composed of persons from one race only (the board H is zero), the further from zero the Hcty, the less representative the board.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Yancey 10182 0.2 0.6 97.7 1.6 0.129 5 0 0 5
Clay 6065 0.1 0.2 97.4 2.2 0.133 5 0 0 5
Avery 8326 0.1 0.4 97.2 2.3 0.142 5 0 0 5
Ashe 13637 0.1 0.4 97.2 2.3 0.145 5 0 0 5
Mitchell 8164 0.1 0.2 96.7 3.0 0.155 5 0 0 5
Macon 17882 0.2 0.5 96.9 2.4 0.157 5 0 0 5
Cherokee 14270 0.6 0.7 97.0 1.8 0.164 5 0 0 5
Alleghany 5376 0.1 1.1 96.5 2.3 0.178 5 0 0 5
McDowell 19960 0.1 2.6 96.0 1.3 0.194 5 0 0 5
Madison 11379 0.1 0.7 95.9 3.3 0.195 5 0 0 5
Haywood 30952 0.2 0.9 96.0 2.9 0.198 5 0 0 5
Dare 19726 0.1 1.6 95.6 2.7 0.214 7 0 0 7
Graham 4243 3.9 0.0 94.5 1.6 0.247 5 0 0 5
Wilkes 31506 0.1 3.5 94.3 2.2 0.261 5 0 0 5
Yadkin 17730 0.1 2.7 94.3 2.9 0.263 5 0 0 5
Alexander 18442 0.1 3.5 94.0 2.3 0.271 5 0 0 5
Transylvania 17985 0.2 2.8 93.8 3.2 0.280 5 0 0 5
Watauga 30243 0.1 1.8 93.4 4.7 0.286 5 0 0 5
Polk 10998 0.1 3.9 93.2 2.8 0.298 5 0 0 5
Stokes 22692 0.2 4.0 93.0 2.8 0.308 5 0 0 5
Henderson 58606 0.1 2.4 92.9 4.6 0.309 5 0 0 5
Caldwell 36536 0.1 4.7 92.8 2.5 0.310 5 0 0 5
Surry 32360 0.1 3.4 92.1 4.4 0.337 5 0 0 5
Carteret 37976 0.2 4.4 91.8 3.7 0.348 7 0 0 7
Currituck 12710 0.2 5.0 91.5 3.2 0.356 7 0 0 7
Burke 39184 0.1 5.8 91.1 3.0 0.362 5 0 0 5
Lincoln 40240 0.1 5.4 90.9 3.6 0.373 5 0 0 5
Davie 21917 0.1 6.0 90.2 3.8 0.392 5 0 0 5
Randolph 64839 0.3 5.7 90.2 3.9 0.398 5 0 0 5
Davidson 75264 0.2 8.6 87.8 3.3 0.452 7 0 0 7
Catawba 72729 0.1 8.0 87.2 4.7 0.473 5 0 0 5
Brunswick 68712 0.2 8.4 87.2 4.1 0.474 5 0 0 5
Jackson 18872 4.0 2.3 88.3 5.4 0.482 5 0 0 5
Rutherford 30477 0.1 9.3 86.5 4.2 0.487 5 0 0 5
Stanly 30095 0.2 9.9 86.2 3.7 0.489 7 0 0 7
Moore 49022 0.4 11.2 85.1 3.3 0.518 5 0 0 5
Camden 5036 0.2 13.8 82.8 3.2 0.551 5 0 0 5
Rowan 64635 0.1 15.0 81.2 3.6 0.584 5 0 0 5
Hyde 2319 0.0 20.2 77.8 1.9 0.598 5 0 0 5
Union 106341 0.2 11.4 81.8 6.6 0.606 5 0 0 5
Pender 27991 0.2 15.3 80.2 4.2 0.612 5 0 0 5
Johnston 86334 0.3 14.9 79.3 5.5 0.643 7 0 0 7
Gaston 96792 0.2 15.3 79.0 5.5 0.646 7 0 0 7
Rockingham 42519 0.2 19.6 76.8 3.5 0.650 5 0 0 5
Montgomery 11618 0.2 20.3 75.0 4.5 0.694 5 0 0 5
Cabarrus 93702 0.2 16.6 76.2 7.0 0.705 5 0 0 5
Alamance 71531 0.3 19.7 73.8 6.3 0.734 5 0 0 5
Onslow 57342 0.3 17.2 74.8 7.8 0.736 5 0 0 5
Jones 5159 0.1 31.8 65.2 2.8 0.752 5 0 0 5
Northampton 9892 0.2 56.3 41.4 2.1 0.782 5 0 5 0
Richmond 19424 1.0 32.4 63.5 3.0 0.807 7 0 0 7
Warren 9883 4.5 52.7 39.8 3.0 0.948 5 0 5 0

Combining Simulations and Diversity Indexes

The two methodologies discussed above, simulation and diversity index, are independent of each other. That is to say that, while that use the same data, their computations have nothing in common. In this section I will combine them in what I feel is a reasonable way and make some interesting observations.

Plots

The following plot shows the counties that were in cluster 1, where the actual board result was a likely result of the turnout simulation.

The next plot shows the counties that were in cluster 2 or 3, where the actual board result was less likely a result of the turnout simulation.

Tables

The 43 counties with Board Diversity Index of zero (that is, where the board is composed of members of a single race category) that are in cluster 1 are shown below in Hcty order, with their turnouts and 2016 board compositions. Since these counties have boards composed of persons from one race only (the board H is zero), the further from zero the Hcty, the turnout Diversity Index, the less representative the board.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Yancey 10182 0.2 0.6 97.7 1.6 0.129 5 0 0 5
Clay 6065 0.1 0.2 97.4 2.2 0.133 5 0 0 5
Avery 8326 0.1 0.4 97.2 2.3 0.142 5 0 0 5
Ashe 13637 0.1 0.4 97.2 2.3 0.145 5 0 0 5
Mitchell 8164 0.1 0.2 96.7 3.0 0.155 5 0 0 5
Macon 17882 0.2 0.5 96.9 2.4 0.157 5 0 0 5
Cherokee 14270 0.6 0.7 97.0 1.8 0.164 5 0 0 5
Alleghany 5376 0.1 1.1 96.5 2.3 0.178 5 0 0 5
McDowell 19960 0.1 2.6 96.0 1.3 0.194 5 0 0 5
Madison 11379 0.1 0.7 95.9 3.3 0.195 5 0 0 5
Haywood 30952 0.2 0.9 96.0 2.9 0.198 5 0 0 5
Dare 19726 0.1 1.6 95.6 2.7 0.214 7 0 0 7
Graham 4243 3.9 0.0 94.5 1.6 0.247 5 0 0 5
Wilkes 31506 0.1 3.5 94.3 2.2 0.261 5 0 0 5
Yadkin 17730 0.1 2.7 94.3 2.9 0.263 5 0 0 5
Alexander 18442 0.1 3.5 94.0 2.3 0.271 5 0 0 5
Transylvania 17985 0.2 2.8 93.8 3.2 0.280 5 0 0 5
Watauga 30243 0.1 1.8 93.4 4.7 0.286 5 0 0 5
Polk 10998 0.1 3.9 93.2 2.8 0.298 5 0 0 5
Stokes 22692 0.2 4.0 93.0 2.8 0.308 5 0 0 5
Henderson 58606 0.1 2.4 92.9 4.6 0.309 5 0 0 5
Caldwell 36536 0.1 4.7 92.8 2.5 0.310 5 0 0 5
Surry 32360 0.1 3.4 92.1 4.4 0.337 5 0 0 5
Carteret 37976 0.2 4.4 91.8 3.7 0.348 7 0 0 7
Currituck 12710 0.2 5.0 91.5 3.2 0.356 7 0 0 7
Burke 39184 0.1 5.8 91.1 3.0 0.362 5 0 0 5
Lincoln 40240 0.1 5.4 90.9 3.6 0.373 5 0 0 5
Davie 21917 0.1 6.0 90.2 3.8 0.392 5 0 0 5
Randolph 64839 0.3 5.7 90.2 3.9 0.398 5 0 0 5
Davidson 75264 0.2 8.6 87.8 3.3 0.452 7 0 0 7
Catawba 72729 0.1 8.0 87.2 4.7 0.473 5 0 0 5
Brunswick 68712 0.2 8.4 87.2 4.1 0.474 5 0 0 5
Jackson 18872 4.0 2.3 88.3 5.4 0.482 5 0 0 5
Rutherford 30477 0.1 9.3 86.5 4.2 0.487 5 0 0 5
Stanly 30095 0.2 9.9 86.2 3.7 0.489 7 0 0 7
Moore 49022 0.4 11.2 85.1 3.3 0.518 5 0 0 5
Camden 5036 0.2 13.8 82.8 3.2 0.551 5 0 0 5
Rowan 64635 0.1 15.0 81.2 3.6 0.584 5 0 0 5
Union 106341 0.2 11.4 81.8 6.6 0.606 5 0 0 5
Pender 27991 0.2 15.3 80.2 4.2 0.612 5 0 0 5
Gaston 96792 0.2 15.3 79.0 5.5 0.646 7 0 0 7
Cabarrus 93702 0.2 16.6 76.2 7.0 0.705 5 0 0 5
Onslow 57342 0.3 17.2 74.8 7.8 0.736 5 0 0 5


The 9 counties with Board Diversity Index of zero that are in clusters 2 or 3 are shown below in Hcty order, with their turnouts and 2016 board compositions. Since they all have boards composed of persons of a single race, and they were in cluster 2 or 3, where the board composition was an unlikely consequence of their turnout proportions, they may all be considered unrepresentative. These counties merit further study.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite
Hyde 2319 0.0 20.2 77.8 1.9 0.598 5 0 0 5
Johnston 86334 0.3 14.9 79.3 5.5 0.643 7 0 0 7
Rockingham 42519 0.2 19.6 76.8 3.5 0.650 5 0 0 5
Montgomery 11618 0.2 20.3 75.0 4.5 0.694 5 0 0 5
Alamance 71531 0.3 19.7 73.8 6.3 0.734 5 0 0 5
Jones 5159 0.1 31.8 65.2 2.8 0.752 5 0 0 5
Northampton 9892 0.2 56.3 41.4 2.1 0.782 5 0 5 0
Richmond 19424 1.0 32.4 63.5 3.0 0.807 7 0 0 7
Warren 9883 4.5 52.7 39.8 3.0 0.948 5 0 5 0


The remaining 10 counties in this plot are in the following list. They are arranged by the difference between the county turnout H and the board H, in ascending order. These counties have boards composed of more than one race, and are in cluster 2 or 3, the less likely simulation compositions. These counties are of less pronounced representation concerns than those discussed immediately above but may merit further study.

County Total AmIndPct BlackPct WhitePct OtherPct Hcty ncomm namin nafam nwhite Hboard Hdiff
Perquimans 6737 0.2 21.9 75.9 2.0 0.631 6 0 2 4 0.637 -0.006
Iredell 82961 0.2 10.6 84.9 4.3 0.523 5 0 1 4 0.500 0.023
Swain 6202 13.9 0.5 83.7 2.0 0.528 5 1 0 4 0.500 0.028
Buncombe 140014 0.2 5.0 88.4 6.4 0.448 7 0 1 6 0.410 0.037
New Hanover 112533 0.2 11.6 81.9 6.3 0.600 5 0 1 4 0.500 0.100
Hoke 18289 5.6 42.0 44.8 7.6 1.081 5 1 3 1 0.950 0.131
Bertie 9389 0.1 56.8 39.7 3.3 0.809 5 0 2 3 0.673 0.136
Chatham 40149 0.2 11.7 79.9 8.2 0.646 5 0 1 4 0.500 0.146
Cleveland 44832 0.1 20.7 76.1 3.1 0.650 5 1 0 4 0.500 0.149
Columbus 23804 2.3 29.1 66.7 1.9 0.792 7 0 1 6 0.410 0.381


Appendix A: Comments on the American Indian Population

In 2016, 4 counties reported American Indian board members. The following table shows characteristics of these counties. By way of comparison, the median American Indian population in 2016 was 282.5 and UH, the “upper hinge” (one-and-a-half times the interquartile distance above the median), was 736.5. There were 25 counties with American Indian populations above the upper hinge.

County Ncomm AmInd Black White total_AmInd total_Black total_White above_UH
Cleveland 5 1 0 4 221 20151 73303 No
Hoke 5 1 3 1 4281 17275 23751 Yes
Robeson 8 3 2 3 52120 32599 39500 Yes
Swain 5 1 0 4 3952 186 9143 Yes
Table 1: (above) Counties with American Indian Commissioners 2016

The next table shows some characteristics of the 10 counties with the highest American Indian population.

County Total AmInd Black White Other N_AmInd
Halifax 52849 1901 27527 21187 2234 0
Columbus 57015 2111 17625 35133 2146 0
Guilford 511815 2297 171837 288612 49069 0
Mecklenburg 1011774 3181 315272 565183 128138 0
Wake 998576 3405 205682 669687 119802 0
Jackson 41227 3504 1274 34411 2038 0
Scotland 35711 3777 13730 16249 1955 0
Swain 14234 3952 186 9143 953 1
Hoke 51853 4281 17275 23751 6546 1
Cumberland 325841 4738 120092 166292 34719 0
Robeson 134576 52120 32599 39500 10357 3
Table 2: (above) Counties with Highest American Indian Population 2016

Conditioning on American Indian Voter Turnout

In this section I make similar observations about American Indian representation, but looking at voter turnout instead of population estimates.

The following table shows voter turnout characteristics of the counties that had American Indian board members. By way of comparison, the median American Indian voter turnout in 2016 was 57.5 and UHT, the “upper hinge” (one-and-a-half times the interquartile distance above the median), was 193.5.

County Ncomm AmInd Black White total_AmInd total_Black total_White above_UHT
Cleveland 5 1 0 4 52 9269 34113 No
Hoke 5 1 3 1 1028 7675 8199 Yes
Robeson 8 3 2 3 12558 12212 14759 Yes
Swain 5 1 0 4 859 34 5188 Yes
Table 3: (above) American Indian Voter Turnout 2016

The next table shows some characteristics of the 10 counties with the highest American Indian 2016 turnout.

County Total AmInd Black White Other N_AmInd
Columbus 23804 538 6932 15873 461 0
Guilford 258714 603 84874 155460 17777 0
Halifax 25205 737 13244 10475 749 0
Jackson 18872 752 432 16672 1016 0
Scotland 13988 764 5633 7084 507 0
Swain 6202 859 34 5188 121 1
Hoke 18289 1028 7675 8199 1387 1
Mecklenburg 475593 1155 147732 281907 44799 0
Wake 531248 1202 96385 368296 65365 0
Cumberland 128007 1207 53965 59561 13274 0
Robeson 41137 12558 12212 14759 1608 3
Table 4: (above) Counties with Highest American Indian Turnout 2016

Observations on American Indian Representation

Cleveland county, with a very small American Indian population, had one commissioner from that race category in 2016. Since there are five commissioners, the representation was twenty percent as compared to the 0.2% population proportion. The proportion of American Indian voters was 0.1%. The disproportion of board membership is an expression of the small number of commissioners.

Robeson county had eight commissioners with three being American Indian in 2016. This was 38% of the board, while the population proportion was 39%. The proportion of American Indian voters was 30.5%. The difference between five and eight commissioners moves the proportions from multiples of 20% to multiples of 12.5%, which can have a substantial impact on representation proportions.

Appendix B: Characterization of the Clusters

Clustering makes most sense if the underlying proportion data has features. The inference here is that the county turnouts that are more or less uniform would result in larger numbers of board compositions that are likely, that is, the number of board compositions that constitute a cluster. If cluster 1, which contains the most likely board compositions, contains many individual instances, the uniqueness of the clustering would be less than if it contained fewer instances. The clustering computation yields a measure, the withinss, the sum of squares of distances from a centroid, that can be used to make comparisons of this uniqueness.

I have scaled the withinss by dividing by the ratio of the county turnout to the minimum of all turnouts. I present in the following plot the log of the scaled withinss. The counties grouped horizontally at the bottom all have a cluster 1 with only one member Npct, that is, the simulation results in a unique match to the actual board. Counties toward the top of the plot, with cluster 1 having the highest scaled withinss, should be associated with counties that have greater numbers of simulated board compositions in cluster 1.



Here is a list of the cluster 1 counties arranged in descending order by the scaled withinss. Larger values correspond to more spread out clusters, that is, clusters that contain more potential board configurations.

County Total withinss withinss_scaled
Gaston 96792 39935537.9 13.489257
Sampson 26069 26853799.9 14.404215
Gates 5420 25716914.8 15.931608
Greene 8123 25481069.5 15.517791
Orange 82814 23898037.4 13.131754
Caswell 11123 20567393.0 14.989247
Wilson 38273 19200214.0 13.684731
Cabarrus 93702 17942042.8 12.721582
Pitt 80865 17328732.6 12.834140
Edgecombe 24961 17325610.0 14.009426
Craven 47235 17268693.8 13.368315
Rowan 64635 16289624.3 12.996327
Lee 25212 16076837.4 13.924614
Lenoir 27008 15522479.1 13.820711
Scotland 13988 15054672.6 14.448043
Chowan 7254 13831218.6 15.019930
Duplin 20928 12764121.6 13.880105
Granville 27481 11398572.5 13.494548
Guilford 258714 10519733.3 11.172084
Forsyth 179297 10503898.3 11.537258
Tyrrell 1749 9784847.0 16.096346
Wayne 50945 9375816.6 12.681942
Hertford 10205 8422948.7 14.182637
Vance 20041 8099576.5 13.468586
Wake 531248 8050385.0 10.185046
Franklin 30563 7708746.3 12.997120
Onslow 57342 7177063.5 12.296412
Bladen 15955 4964890.4 13.207174
Pender 27991 4696212.8 12.589428
Nash 47878 4081620.3 11.912393
Cumberland 128007 3906062.0 10.884999
Mecklenburg 475593 3900482.7 9.571093
Washington 6178 3730614.4 13.870133
Anson 10598 2354865.2 12.870373
Halifax 25205 1112178.3 11.253833
Beaufort 24054 734537.4 10.885739
Robeson 41137 592081.4 10.133536
Pasquotank 17462 119975.3 9.394058
Alexander 18442 0.0 1.000000
Alleghany 5376 0.0 1.000000
Ashe 13637 0.0 1.000000
Avery 8326 0.0 1.000000
Brunswick 68712 0.0 1.000000
Burke 39184 0.0 1.000000
Caldwell 36536 0.0 1.000000
Camden 5036 0.0 1.000000
Carteret 37976 0.0 1.000000
Catawba 72729 0.0 1.000000
Cherokee 14270 0.0 1.000000
Clay 6065 0.0 1.000000
Currituck 12710 0.0 1.000000
Dare 19726 0.0 1.000000
Davidson 75264 0.0 1.000000
Davie 21917 0.0 1.000000
Durham 156843 0.0 1.000000
Graham 4243 0.0 1.000000
Harnett 46276 0.0 1.000000
Haywood 30952 0.0 1.000000
Henderson 58606 0.0 1.000000
Jackson 18872 0.0 1.000000
Lincoln 40240 0.0 1.000000
McDowell 19960 0.0 1.000000
Macon 17882 0.0 1.000000
Madison 11379 0.0 1.000000
Martin 12012 0.0 1.000000
Mitchell 8164 0.0 1.000000
Moore 49022 0.0 1.000000
Pamlico 6904 0.0 1.000000
Person 19736 0.0 1.000000
Polk 10998 0.0 1.000000
Randolph 64839 0.0 1.000000
Rutherford 30477 0.0 1.000000
Stanly 30095 0.0 1.000000
Stokes 22692 0.0 1.000000
Surry 32360 0.0 1.000000
Transylvania 17985 0.0 1.000000
Union 106341 0.0 1.000000
Watauga 30243 0.0 1.000000
Wilkes 31506 0.0 1.000000
Yadkin 17730 0.0 1.000000
Yancey 10182 0.0 1.000000

Appendix C: Supplement to the Entropy Index Analysis

I have rearranged the diversity indexes in the following plot. This shows the difference between the county and the board indexes. The numeric value of this difference has no useful interpretation. The significance is in suggesting which counties to pursue further.

Appendix D: Quick List of County Populations as ACS Estimates

This is for 2016.

County FIPS3 Total AmInd Black White Other AmIndPct BlackPct WhitePct OtherPct Hcty
Alamance 001 156372 621 29039 110548 16164 0.4 18.6 70.7 10.3 0.8144
Alexander 003 37211 114 2142 33005 1950 0.3 5.8 88.7 5.2 0.4430
Alleghany 005 10868 170 262 9936 500 1.6 2.4 91.4 4.6 0.3785
Anson 007 25883 86 12612 12423 762 0.3 48.7 48.0 2.9 0.8254
Ashe 009 26992 92 193 25354 1353 0.3 0.7 93.9 5.0 0.2635
Avery 011 17633 86 655 16209 683 0.5 3.7 91.9 3.9 0.3516
Beaufort 013 47513 54 12331 33458 1670 0.1 26.0 70.4 3.5 0.7224
Bertie 015 20324 127 12608 7313 276 0.6 62.0 36.0 1.4 0.7541
Bladen 017 34454 817 12086 19831 1720 2.4 35.1 57.6 5.0 0.9238
Brunswick 019 119167 506 12589 99521 6551 0.4 10.6 83.5 5.5 0.5706
Buncombe 021 250112 886 15713 222134 11379 0.4 6.3 88.8 4.5 0.4398
Burke 023 89082 459 5483 75155 7985 0.5 6.2 84.4 9.0 0.5584
Cabarrus 025 192296 568 32188 142064 17476 0.3 16.7 73.9 9.1 0.7580
Caldwell 027 81623 442 3998 73059 4124 0.5 4.9 89.5 5.1 0.4260
Camden 029 10228 23 1450 8452 303 0.2 14.2 82.6 3.0 0.5525
Carteret 031 68537 258 4157 60921 3201 0.4 6.1 88.9 4.7 0.4388
Caswell 033 23094 41 7518 14408 1127 0.2 32.6 62.4 4.9 0.8183
Catawba 035 155461 443 13304 123873 17841 0.3 8.6 79.7 11.5 0.6565
Chatham 037 68778 185 8218 55295 5080 0.3 11.9 80.4 7.4 0.6376
Cherokee 039 27226 398 375 25518 935 1.5 1.4 93.7 3.4 0.2973
Chowan 041 14556 178 4889 9163 326 1.2 33.6 62.9 2.2 0.7967
Clay 043 10730 0 45 10646 39 0.0 0.4 99.2 0.4 0.0512
Cleveland 045 97113 221 20151 73303 3438 0.2 20.8 75.5 3.5 0.6708
Columbus 047 57015 2111 17625 35133 2146 3.7 30.9 61.6 3.8 0.9068
Craven 049 104190 699 22365 73456 7670 0.7 21.5 70.5 7.4 0.8023
Cumberland 051 325841 4738 120092 166292 34719 1.5 36.9 51.0 10.7 1.0113
Currituck 053 24864 140 1550 22490 684 0.6 6.2 90.5 2.8 0.3918
Dare 055 35187 94 707 32040 2346 0.3 2.0 91.1 6.7 0.3602
Davidson 057 164058 669 14750 141859 6780 0.4 9.0 86.5 4.1 0.4964
Davie 059 41568 21 2635 36842 2070 0.1 6.3 88.6 5.0 0.4350
Duplin 061 59121 114 14724 38153 6130 0.2 24.9 64.5 10.4 0.8759
Durham 063 294618 1091 110777 150067 32683 0.4 37.6 50.9 11.1 0.9761
Edgecombe 065 54669 216 30998 21006 2449 0.4 56.7 38.4 4.5 0.8502
Forsyth 067 364691 780 95187 242803 25921 0.2 26.1 66.6 7.1 0.8225
Franklin 069 62989 808 16230 42412 3539 1.3 25.8 67.3 5.6 0.8334
Gaston 071 211753 824 32627 162526 15776 0.4 15.4 76.8 7.5 0.7063
Gates 073 11615 96 3837 7363 319 0.8 33.0 63.4 2.7 0.7932
Graham 075 8651 704 34 7681 232 8.1 0.4 88.8 2.7 0.4286
Granville 077 58341 356 17960 35739 4286 0.6 30.8 61.3 7.3 0.8858
Greene 079 21241 102 7554 11960 1625 0.5 35.6 56.3 7.7 0.9134
Guilford 081 511815 2297 171837 288612 49069 0.4 33.6 56.4 9.6 0.9385
Halifax 083 52849 1901 27527 21187 2234 3.6 52.1 40.1 4.2 0.9595
Harnett 085 126620 1137 26921 85578 12984 0.9 21.3 67.6 10.3 0.8698
Haywood 087 59577 167 637 57137 1636 0.3 1.1 95.9 2.7 0.2038
Henderson 089 110905 219 3488 101051 6147 0.2 3.1 91.1 5.5 0.3662
Hertford 091 24285 260 14144 8572 1309 1.1 58.2 35.3 5.4 0.8884
Hoke 093 51853 4281 17275 23751 6546 8.3 33.3 45.8 12.6 1.1910
Hyde 095 5629 10 1855 3743 21 0.2 33.0 66.5 0.4 0.6692
Iredell 097 167493 749 20622 136625 9497 0.4 12.3 81.6 5.7 0.6110
Jackson 099 41227 3504 1274 34411 2038 8.5 3.1 83.5 4.9 0.6165
Johnston 101 182155 962 27836 142427 10930 0.5 15.3 78.2 6.0 0.6759
Jones 103 10074 35 3080 6634 325 0.3 30.6 65.9 3.2 0.7679
Lee 105 59540 405 11332 41679 6124 0.7 19.0 70.0 10.3 0.8333
Lenoir 107 58343 209 22838 32054 3242 0.4 39.1 54.9 5.6 0.8770
Lincoln 109 79783 188 4271 70542 4782 0.2 5.4 88.4 6.0 0.4485
McDowell 111 45013 238 1804 40968 2003 0.5 4.0 91.0 4.4 0.3808
Macon 113 33991 161 391 31469 1970 0.5 1.2 92.6 5.8 0.3132
Madison 115 21130 36 407 20310 377 0.2 1.9 96.1 1.8 0.1968
Martin 117 23510 81 10162 12711 556 0.3 43.2 54.1 2.4 0.8031
Mecklenburg 119 1011774 3181 315272 565183 128138 0.3 31.2 55.9 12.7 0.9684
Mitchell 121 15263 92 62 14797 312 0.6 0.4 96.9 2.0 0.1628
Montgomery 123 27475 75 5166 21057 1177 0.3 18.8 76.6 4.3 0.6692
Moore 125 93070 652 11654 77031 3733 0.7 12.5 82.8 4.0 0.5805
Nash 127 94385 624 36659 50234 6868 0.7 38.8 53.2 7.3 0.9269
New Hanover 129 216430 636 30589 175310 9895 0.3 14.1 81.0 4.6 0.6054
Northampton 131 20628 104 11843 8133 548 0.5 57.4 39.4 2.7 0.8086
Onslow 133 185755 937 27888 138029 18901 0.5 15.0 74.3 10.2 0.7646
Orange 135 139807 709 16010 105093 17995 0.5 11.5 75.2 12.9 0.7534
Pamlico 137 12892 148 2374 9722 648 1.1 18.4 75.4 5.0 0.7260
Pasquotank 139 39909 77 14580 23440 1812 0.2 36.5 58.7 4.5 0.8329
Pender 141 56358 243 9219 43164 3732 0.4 16.4 76.6 6.6 0.7037
Perquimans 143 13470 20 3296 9880 274 0.1 24.5 73.3 2.0 0.6607
Person 145 39196 361 10551 26918 1366 0.9 26.9 68.7 3.5 0.7715
Pitt 147 175150 515 60578 102061 11996 0.3 34.6 58.3 6.8 0.8827
Polk 149 20324 45 1084 18530 665 0.2 5.3 91.2 3.3 0.3660
Randolph 151 142588 637 8752 123509 9690 0.4 6.1 86.6 6.8 0.5026
Richmond 153 45710 933 14473 28756 1548 2.0 31.7 62.9 3.4 0.8498
Robeson 155 134576 52120 32599 39500 10357 38.7 24.2 29.4 7.7 1.2680
Rockingham 157 91898 477 17041 69614 4766 0.5 18.5 75.8 5.2 0.7036
Rowan 159 138694 312 22329 108360 7693 0.2 16.1 78.1 5.5 0.6610
Rutherford 161 66701 325 6893 56997 2486 0.5 10.3 85.5 3.7 0.5175
Sampson 163 63713 1219 16240 39660 6594 1.9 25.5 62.2 10.3 0.9539
Scotland 165 35711 3777 13730 16249 1955 10.6 38.4 45.5 5.5 1.1224
Stanly 167 60610 208 6369 51212 2821 0.3 10.5 84.5 4.7 0.5414
Stokes 169 46453 271 1932 43386 864 0.6 4.2 93.4 1.9 0.3002
Surry 171 72767 276 2689 66972 2830 0.4 3.7 92.0 3.9 0.3457
Swain 173 14234 3952 186 9143 953 27.8 1.3 64.2 6.7 0.8778
Transylvania 175 33062 117 1273 29879 1793 0.4 3.9 90.4 5.4 0.3949
Tyrrell 177 4128 85 1512 2302 229 2.1 36.6 55.8 5.5 0.9339
Union 179 217614 724 25260 177613 14017 0.3 11.6 81.6 6.4 0.6114
Vance 181 44508 752 22162 19355 2239 1.7 49.8 43.5 5.0 0.9287
Wake 183 998576 3405 205682 669687 119802 0.3 20.6 67.1 12.0 0.8671
Warren 185 20324 980 10328 8046 970 4.8 50.8 39.6 4.8 1.0022
Washington 187 12503 18 6079 5815 591 0.1 48.6 46.5 4.7 0.8603
Watauga 189 52745 170 632 49587 2356 0.3 1.2 94.0 4.5 0.2684
Wayne 191 124447 289 38504 74099 11555 0.2 30.9 59.5 9.3 0.9064
Wilkes 193 68888 133 2945 62792 3018 0.2 4.3 91.2 4.4 0.3683
Wilson 195 81617 515 31846 41325 7931 0.6 39.0 50.6 9.7 0.9703
Yadkin 197 37819 111 1285 34612 1811 0.3 3.4 91.5 4.8 0.3586
Yancey 199 17599 76 206 16991 326 0.4 1.2 96.5 1.9 0.1834